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Simplifying (6n + 1)(3n + 7) = 0 Reorder the terms: (1 + 6n)(3n + 7) = 0 Reorder the terms: (1 + 6n)(7 + 3n) = 0 Multiply (1 + 6n) * (7 + 3n) (1(7 + 3n) + 6n * (7 + 3n)) = 0 ((7 * 1 + 3n * 1) + 6n * (7 + 3n)) = 0 ((7 + 3n) + 6n * (7 + 3n)) = 0 (7 + 3n + (7 * 6n + 3n * 6n)) = 0 (7 + 3n + (42n + 18n2)) = 0 Combine like terms: 3n + 42n = 45n (7 + 45n + 18n2) = 0 Solving 7 + 45n + 18n2 = 0 Solving for variable 'n'. Factor a trinomial. (7 + 3n)(1 + 6n) = 0Subproblem 1
Set the factor '(7 + 3n)' equal to zero and attempt to solve: Simplifying 7 + 3n = 0 Solving 7 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3n = 0 + -7 3n = 0 + -7 Combine like terms: 0 + -7 = -7 3n = -7 Divide each side by '3'. n = -2.333333333 Simplifying n = -2.333333333Subproblem 2
Set the factor '(1 + 6n)' equal to zero and attempt to solve: Simplifying 1 + 6n = 0 Solving 1 + 6n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6n = 0 + -1 6n = 0 + -1 Combine like terms: 0 + -1 = -1 6n = -1 Divide each side by '6'. n = -0.1666666667 Simplifying n = -0.1666666667Solution
n = {-2.333333333, -0.1666666667}
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